A normal form analysis in a finite neighborhood of a hopf bifurcation: on the center manifold dimension

The problem of determining the bounds of applicability of perturbation expansions in terms both of the system parameters and the state-space variable amplitude is a key point in the perturbation analysis of nonlinear systems. In the present paper an analysis in a finite neighborhood of a Hopf bifurcation is presented in order to analyze the conditions under which a Normal Form zero-divisors-based approach fails to describe the local dynamics and, therefore, a small divisor approach is required. The condition of “smallness” referred to the divisors is analyzed from both a qualitative and a quantitative point of view. Finally, a simple but effective analytical and numerical example is introduced to illustrate the theoretical issues along with an interpretation within a codimension-two framework

Nonlinear aeroelastic modeling via conformal mapping and vortex method for a flat-plate airfoil in arbitrary motion

A nonlinear aerodynamic modeling based on conformal mapping is presented to obtain semi-analytical formulas for the unsteady aerodynamic force and pitching moment on a flat-plate airfoil in arbitrary motion. The aerodynamic model accounts for large amplitudes and non-planar wake and is used to study the aeroelastic behavior of a flat-plate airfoil elastically connected to a support. The fluid is assumed to be inviscid and incompressible, while the flow is assumed to be attached, planar, and potential. Within these hypotheses, conformal mapping and a complex-potential representation of unsteady aerodynamics are used to simplify the theoretical formulation. The vorticity shed at the trailing edge is discretized in desingularized point vortices in order to allow free-wake dynamics. The unsteady aerodynamic model is validated with classical linearized formulations based on the assumption of small disturbances, and with experimental data and theoretical predictions for a large-amplitude pitch-up, hold, pitch-down maneuver. The aeroelastic model is then used to simulate the response of a flat-plate airfoil to sudden starts and body-vortex interactions. Numerical results show that the proposed approach can be an effective tool to model the aeroelastic behavior of an arbitrarily-moving wing section in a time-dependent potential stream of incompressible fluid

OMA analysis of a launcher under operational conditions with time-varying properties

The objective of the paper is the investigation of the capability of Operational Modal Analysis approaches to deal with time-varying system in the low-frequency domain. Specifically, the problem of the identification of the dynamic properties of a launch-vehicle, working under actual operative conditions, is studied. Two OMA methods are considered: the Frequency Domain Decomposition and the Hilbert Transform Method. It is demonstrated that both OMA approaches allow the time-tracking of modal parameters, namely, natural frequencies, damping ratios and mode shapes, from the response accelerations only recorded during actual flight tests of a launcher characterized by a large mass variation due to fuel burning typical of the first phase of the flight

Neural network-based reduced-order modeling for nonlinear vertical sloshing with experimental validation

In this paper, a nonlinear reduced-order model based on neural networks is introduced in order to model vertical sloshing in presence of Rayleigh–Taylor instability of the free surface for use in fluid–structure interaction simulations. A box partially filled with water, representative of a wing tank, is first set on vertical harmonic motion via a controlled electrodynamic shaker. Accelerometers and load cells at the interface between the tank and an electrodynamic shaker are employed to train a neural network-based reduced-order model for vertical sloshing. The model is then investigated for its capacity to consistently simulate the amount of dissipation associated with vertical sloshing under different fluid dynamics regimes. The identified tank is then experimentally attached at the free end of a cantilever beam to test the effectiveness of the neural network in predicting the sloshing forces when coupled with the overall structure. The experimental free response and random seismic excitation responses are then compared with that obtained by simulating an equivalent virtual model in which the identified nonlinear reduced-order model is integrated to account for the effects of violent vertical sloshing

Experimental Validation of Neural-Network-Based Nonlinear Reduced-Order Model for Vertical Sloshing

In this paper, a nonlinear reduced order model based on neural networks is introduced in order to model vertical sloshing for use in fluid-structure interaction simulations. A box partially filled with water, representative of a wing tank, is first tested to identify a neural network model and then attached to a cantilever beam to test the effectiveness of the neural network in predicting the sloshing forces when coupled with the structure. The experimental set-up is equipped with accelerometers and load cells at the interface between the tank and an electrodynamic shaker, which provides vertical acceleration to the tank. Accelerations and interface forces measured during the experimental tests are employed to identify a recurrent network able to return the vertical sloshing forces when the tank is set on vertical motion. The identified model is then experimentally tested and assessed by its integration on the tip of a cantilever beam. The free response of the experimental setup are compared with those obtained by simulating an equivalent virtual model in which the identified reduced-order model is integrated to account for the effects of vertical sloshing

Analysis of helicopter cabin vibrations due to rotor asymmetry and gust encounter

The availability of a numerical tool capable to predict the vibration level inside the cabin due to main rotor-fuselage interaction is of great importance in helicopter design. Indeed, it would be a source of information concerning the fatigue-life of the structure, that in turn would allow a rough estimate of consequent maintenance costs. Furthermore, such a tool would be helpful also in the process of identifying design solutions aimed to the interior noise reduction, that is a crucial aspect for the widely-requested passenger comfort enhancement. In this paper, the simulation tool is obtained as a finite element structural dynamic model of the helicopter fuselage forced by vibratory hub loads, that are predicted through the aeroelastic analysis of the main rotor treated as isolated. In particular, the emphasis is on the evaluation of the incremental vibration level induced by rotor asymmetry and gust encounter, that could give raise to interior acoustic patterns annoying for passengers and to vibration peaks dangerous in terms of structural fatigue. All the results are obtained for two different flight conditions

multiphysics numerical investigation on the aeroelastic stability of a le mans prototype car

Abstract In the analysis and design of racing competition cars, numerical tools allow to investigate a wide range of solutions in short time and with high confidence in results. The great available computational power permits to combine simulation software so that different physics involved can be tackled at the same time. An important class of multi-physics simulations for motor sport addresses the fluid-structure interactions happening between the aerodynamic components of the car and the surrounding flow: this interaction can induce structural deformations and vibrations which, in turn, can influence the surrounding fluxes. In this paper, the flutter analysis of the front wing splitter mounted on the 2001 Le Mans Prototype car by Dallara (LMP1) is presented. The study was set up adopting high fidelity CAE models: a 400k shell elements FEM represents the full front wing assembly including the mounting frame, a 240M cells CFD represents the full car immersed in a box shaped wind tunnel. FEM extracted structural modal shapes are mapped onto the CFD mesh adopting Radial Basis Functions (RBF) mesh morphing so that the surfaces of the CFD model can be deformed according to retained modes. Such deformation is then propagated so that the volume mesh is adapted accordingly. The elastic CFD model with modes embedded was then loaded by applying a transient signal individually to each retained mode with a smoothed step function. A Reduced Order Model (ROM) for the aerodynamics of the coupled system was then extracted combining the results of the individual transient run. The critical speed experimentally observed to be in the operating range of the car was captured by the model quite well. The same workflow was then adopted to investigate a different design in which a stiffener has been introduced to increase the first mode natural frequency from 40Hz to 49.4Hz. Flutter speed was increased and moved outside the vehicle range. The car equipped with the improved part proved to perform on the track without previously detected instabilities

Sloshing reduced-order model trained with Smoothed Particle Hydrodynamics simulations

The main goal of this paper is to provide a Reduced Order Model (ROM) able to predict the liquid induced dissipation of the violent and vertical sloshing problem for a wide range of liquid viscosities, surface tensions and tank filling levels. For that purpose, the Delta Smoothed Particle Hydrodynamics (δ-SPH) formulation is used to build a database of simulation cases where the physical parameters of the liquid are varied. For each simulation case, a bouncing ball-based equivalent mechanical model is identified to emulate sloshing dynamics. Then, an interpolating hypersurface-based ROM is defined to establish a mapping between the considered physical parameters of the liquid and the identified ball models. The resulting hypersurface effectively estimates the bouncing ball design parameters while considering various types of liquids, producing results consistent with SPH test simulations. Additionally, it is observed that the estimated bouncing ball model not only matches the liquid induced dissipation but also follows the liquid center of mass and presents the same sloshing force and phase-shift trends when varying the tank filling level. These findings provide compelling evidence that the identified ROM is a practical tool for accurately predicting critical aspects of the vertical sloshing problem while requiring minimal computational resources